A Remark on Uniqueness of Large Solutions for Elliptic Systems of Competitive Type ∗ †

@inproceedings{GaraMelin2009ARO,
  title={A Remark on Uniqueness of Large Solutions for Elliptic Systems of Competitive Type ∗ †},
  author={Jorge Gar{\'c}ıa-Meli{\'a}n},
  year={2009}
}
  • Jorge Garćıa-Melián
  • Published 2009
We prove that the semilinear system ∆u = a(x)upvq, ∆v = b(x)urvs in a smooth bounded domain Ω ⊂ RN has a unique positive solution with the boundary condition u = v = +∞ on ∂Ω, provided that p, s > 1, q, r > 0 and (p− 1)(s− 1)− qr > 0. The main novelty is imposing a growth on the possibly singular weights a(x), b(x) near ∂Ω, rather than requiring them to have a precise asymptotic behavior. 

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